1
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The equation of a particle executing simple harmonic motion is given by $$x = \sin \pi \left( {t + {1 \over 3}} \right)m$$. At t = 1s, the speed of particle will be

(Given : $$\pi$$ = 3.14)

A
0 cm s$$-$$1
B
157 cm s$$-$$1
C
272 cm s$$-$$1
D
314 cm s$$-$$1
2
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

A
6 s
B
8 s
C
12 s
D
36 s
3
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $${g \over 6}$$ vertically upwards then the time period will be :

(Where g = acceleration due to gravity)

A
$$\sqrt {{6 \over 5}} T$$
B
$$\sqrt {{5 \over 6}} T$$
C
$$\sqrt {{6 \over 7}} T$$
D
$$\sqrt {{7 \over 6}} T$$
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

A
10 m/s2
B
5 m/s2
C
4 m/s2
D
9.8 m/s2
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